Standard +0.8 This is a Further Maths polar coordinates question requiring sketching and area calculation using integration by parts. While the integral ∫₀^π (θ sin θ)²/2 dθ requires multiple integration techniques (expanding, using double angle formula, then integration by parts), it's a standard application of the polar area formula with moderately complex algebra rather than requiring novel insight.
7 The curve \(C\) has polar equation
$$r = \theta \sin \theta ,$$
where \(0 \leqslant \theta \leqslant \pi\). Draw a sketch of \(C\).
Find the area of the region enclosed by \(C\), leaving your answer in terms of \(\pi\).
7 The curve $C$ has polar equation
$$r = \theta \sin \theta ,$$
where $0 \leqslant \theta \leqslant \pi$. Draw a sketch of $C$.
Find the area of the region enclosed by $C$, leaving your answer in terms of $\pi$.
\hfill \mbox{\textit{CAIE FP1 2007 Q7 [9]}}